Symbol grounding

Harnad, S. (1990) The Symbol Grounding Problem. Physica D 42: 335-346.
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                THE SYMBOL GROUNDING PROBLEM

                Stevan Harnad
                Department of Psychology 
                Princeton University
                Princeton NJ 08544

ABSTRACT:  There has been much discussion recently about the scope and
limits of purely symbolic models of the mind and about the proper role
of connectionism in cognitive modeling. This paper describes the
"symbol grounding problem": How can the semantic interpretation of a
formal symbol system be made
 intrinsic to the system, rather than just parasitic on the meanings in
our heads? How can the meanings of the meaningless symbol tokens,
manipulated solely on the basis of their (arbitrary) shapes, be
grounded in anything but other meaningless symbols? The problem is
analogous to trying to learn Chinese from a Chinese/Chinese dictionary
alone. A candidate solution is sketched: Symbolic representations must
be grounded bottom-up in nonsymbolic representations of two kinds:  (1)
 "iconic representations" , which are analogs of the proximal sensory
projections of distal objects and events, and (2)
 "categorical representations" , which are learned and innate
feature-detectors that pick out the invariant features of object and
event categories from their sensory projections. Elementary symbols are
the names of these object and event categories, assigned on the basis
of their (nonsymbolic) categorical representations. Higher-order (3)
 "symbolic representations" , grounded in these elementary symbols,
consist of symbol strings describing category membership relations
(e.g., "An X is a Y that is Z").
Connectionism is one natural candidate for the mechanism that learns
the invariant features underlying categorical representations, thereby
connecting names to the proximal projections of the distal objects they
stand for. In this way connectionism can be seen as a complementary
component in a hybrid nonsymbolic/symbolic model of the mind, rather
than a rival to purely symbolic modeling. Such a hybrid model would not
have an autonomous symbolic "module," however; the symbolic functions
would emerge as an intrinsically "dedicated" symbol system as a
consequence of the bottom-up grounding of categories' names in their
sensory representations. Symbol manipulation would be governed not just
by the arbitrary shapes of the symbol tokens, but by the nonarbitrary
shapes of the icons and category invariants in which they are grounded.

KEYWORDS: symbol systems, connectionism, category learning, cognitive
models, neural models

1. Modeling the Mind

"1.1 From Behaviorism to Cognitivism." For many years the only
empirical approach in psychology was behaviorism, its only explanatory
tools input/input and input/output associations (in the case of
classical conditioning; Turkkan 1989) and the reward/punishment history
that "shaped" behavior (in the case of operant conditioning; Catania &
Harnad 1988). In a reaction against the subjectivity of armchair
introspectionism, behaviorism had declared that it was just as illicit
to theorize about what went on in the
 head of the organism to generate its behavior as to theorize about
what went on in its
 mind. Only observables were to be the subject matter of psychology;
and, apparently, these were expected to explain themselves.

Psychology became more like an empirical science when, with the gradual
advent of cognitivism (Miller 1956, Neisser 1967, Haugeland 1978), it
became acceptable to make inferences about the
 unobservable processes underlying behavior.
Unfortunately, cognitivism let mentalism in again
by the back door too, for the hypothetical internal processes came
embellished with subjective interpretations. In fact, semantic interpretability
(meaningfulness),
as we shall see, was one of the defining features of the most prominent
contender vying to become the theoretical vocabulary of cognitivism,
the "language of thought" (Fodor 1975), which became the prevailing
view in cognitive theory for several decades in the form of the
"symbolic" model of the mind: The mind is a symbol system and cognition
is symbol manipulation. The possibility of generating complex behavior
through symbol manipulation was empirically demonstrated by successes
in the field of artificial intelligence (AI).

"1.2 Symbol Systems."
 What is a symbol system? From Newell (1980) Pylyshyn (1984), Fodor
(1987) and the classical work of Von Neumann, Turing, Goedel, Church,
etc. (see Kleene 1969) on the foundations of computation, we can
reconstruct the following definition:

A symbol system is:

(1) a set of arbitrary
 "physical tokens" (scratches on paper, holes on a tape, events in a
digital computer, etc.) that are

(2) manipulated on the basis of "explicit rules" that are

(3) likewise physical tokens and strings of tokens. The rule-governed
symbol-token manipulation is based

(4) purely on the shape of the symbol tokens (not their "meaning"),
i.e., it is purely syntactic, and consists of

(5) "rulefully combining" and recombining symbol tokens. There are

(6) primitive atomic symbol tokens and

(7) composite symbol-token strings. The entire system and all its parts
-- the atomic tokens, the composite tokens, the syntactic manipulations
(both actual and possible) and the rules -- are all

(8) "semantically interpretable:" The syntax can be systematically
assigned a meaning (e.g., as standing for objects, as describing states
of affairs).

According to proponents of the symbolic model of mind such as Fodor
(1980) and Pylyshyn (1980, 1984), symbol-strings of this sort capture
what mental phenomena such as thoughts and beliefs are. Symbolists
emphasize that the symbolic level (for them, the mental level) is a
natural functional level of its own, with ruleful regularities that are
independent of their specific physical realizations. For symbolists,
this implementation-independence is the critical difference between
cognitive phenomena and ordinary physical phenomena and their
respective explanations. This concept of an autonomous symbolic level
also conforms to general foundational principles in the theory of
computation and applies to all the work being done in symbolic AI, the
branch of science that has so far been the most successful in
generating (hence explaining) intelligent behavior.

All eight of the properties listed above seem to be critical to this
definition of symbolic.\**
[footnote start]
Paul Kube (personal communication) has suggested that (2) and (3) may
be too strong, excluding some kinds of Turing Machine and perhaps even
leading to an infinite regress on levels of explicitness and
systematicity.
[footnote end]
Many phenomena have some of the properties, but that does not entail
that they are symbolic in this explicit, technical sense. It is not
enough, for example, for a phenomenon to be
 interpretable as rule-governed, for just about anything can be
interpreted as rule-governed. A thermostat may be interpreted as
following the rule: Turn on the furnace if the temperature goes below
70 degrees and turn it off if it goes above 70 degrees, yet nowhere in
the thermostat is that rule explicitly represented.
Wittgenstein (1953) emphasized the difference between
 explicit and implicit rules: It is not the same thing to "follow" a rule
(explicitly) and merely to behave "in accordance with" a rule
(implicitly).\** [footnote start]

Similar considerations apply to Chomsky's (1980) concept of
"psychological reality" (i. e., whether Chomskian rules are really
physically represented in the brain or whether they merely "fit" our
performance regularities, without being what actually governs them).
Another version of the distinction concerns explicitly represented
rules versus hard-wired physical constraints (Stabler 1985). In each
case, an explicit representation consisting of elements that can be
recombined in systematic ways would be symbolic whereas an implicit
physical constraint would not, although
 both would be semantically "intepretable" as a "rule" if construed in
isolation rather than as part of a system.
[footnote end]
The critical
difference is in the compositeness (7) and systematicity (8) criteria.
The explicitly represented symbolic rule is part of a formal system, it is
decomposable (unless primitive), its application and manipulation is
purely formal (syntactic, shape-dependent), and the entire system must be
semantically interpretable, not just the chunk in question. An isolated
("modular") chunk cannot be symbolic; being symbolic is a systematic property.

So the mere fact that a behavior is "interpretable" as
ruleful does not mean that it is really governed by a symbolic rule.\**
[footnote start]



Analogously, the mere fact that a behavior is 
 interpretable
as purposeful
or conscious or meaningful does not mean that it really is purposeful
or conscious. (For arguments to the contrary, see Dennett 1983).
[footnote end]
Semantic interpretability must be coupled with explicit representation
(2), syntactic manipulability (4), and systematicity (8) in order to be
symbolic. None of these criteria is arbitrary, and, as far as I can
tell, if you weaken them, you lose the grip on what looks like a
natural category and you sever the links with the formal theory of
computation, leaving a sense of "symbolic" that is merely unexplicated
metaphor (and probably differs from speaker to speaker). Hence it is
only this formal sense of "symbolic" and "symbol system" that will be
considered in this discussion of the grounding of symbol systems.

"1.3 Connectionist systems."
An early rival to the symbolic model of mind appeared (Rosenblatt 1962),
was overcome by symbolic AI (Minsky & Papert 1969) and has recently
re-appeared in a stronger form that is currently vying with AI to be
the general
theory of cognition and behavior (McClelland, Rumelhart et al. 1986,
Smolensky 1988).
Variously described as "neural networks,"
"parallel distributed processing" and "connectionism," this approach
has a multiple agenda, which includes providing a theory of brain
function. Now, much can be said for and against studying behavioral and
brain function independently, but in this paper it will be assumed
that, first and foremost, a cognitive theory must stand on its own
merits, which depend on how well it explains our observable behavioral
capacity. Whether or not it does so in a sufficiently brainlike way is
another matter, and a downstream one, in the course of theory
development. Very little is known of the brain's structure and its
"lower" (vegetative) functions so far; and the nature of "higher" brain
function is itself a theoretical matter. To "constrain" a cognitive
theory to account for behavior in a brainlike way is hence premature in
two respects: (1) It is far from clear yet what "brainlike" means, and
(2) we are far from having accounted for a lifesize chunk of behavior
yet, even without added constraints.
Moreover, the formal principles underlying connectionism seem to be based on
the associative and statistical structure of the causal interactions
in certain dynamical systems; a neural network is merely one
possible implementation of such a dynamical system.\**
[footnote start]



It is not even clear yet that a "neural network" needs to be
implemented as a net (i.e., a parallel system of interconnected units)
in order to do what it can do; if symbolic simulations of nets have
the same functional capacity as real nets, then a connectionist model
is just a special kind of symbolic model, and connectionism is just a special
family of symbolic algorithms.
[footnote end]

Connectionism will accordingly only be considered here as a cognitive
theory. As such, it has lately challenged the symbolic approach
to modeling the mind. According to connectionism, cognition is not
symbol manipulation but dynamic patterns of activity in a multilayered
network of nodes or units with weighted positive and negative
interconnections. The patterns change according to internal network
constraints governing how the activations and connection strengths are
adjusted on the basis of new inputs (e.g., the generalized "delta
rule," or "backpropagation," McClelland, Rumelhart et al. 1986). The
result is a system that learns, recognizes patterns, solves problems,
and can even exhibit motor skills.

"1.4 Scope and Limits of Symbols and Nets."
It is far from clear what the actual capabilities and limitations of
either symbolic AI or connectionism are. The former seems better at
formal and language-like tasks, the latter at sensory, motor and
learning tasks, but there is considerable overlap and neither has gone
much beyond the stage of "toy" tasks toward lifesize behavioral
capacity. Moreover, there has been some disagreement as to whether or
not connectionism itself is symbolic. We will adopt the position here
that it is not, because connectionist networks fail to meet several of
the criteria for being symbol systems, as Fodor & Pylyshyn (1988) have
argued recently.
In particular, although, like everything else, their behavior and
internal states can be given isolated semantic interpretations, nets
fail to meet the compositeness (7) and systematicity (8) criteria
listed earlier:  The patterns of interconnections do not decompose,
combine and recombine according to a formal syntax that can be given a
systematic semantic interpretation.\**
[footnote start]



There is some misunderstanding of this point because it is often
conflated with a mere implementational issue: Connectionist
networks can be simulated using symbol systems, and symbol systems can
be implemented using a connectionist architecture, but that is
independent of the question of what each can do
 qua
symbol system or connectionist network, respectively. By way of
analogy, silicon can be used to build a computer, and a computer can
simulate the properties of silicon, but the functional
properties of silicon are not those of computation, and the functional
properties of computation are not those of silicon.
[footnote end]
Instead, nets seem to do what they do
 non symbolically.
According to
Fodor & Pylyshyn, this is a severe limitation, because many of our
behavioral capacities appear to be symbolic, and hence the most natural
hypothesis about the underlying cognitive processes that generate them
would be that they too must be symbolic. Our linguistic capacities are
the primary examples here, but many of the other skills we have --
logical reasoning, mathematics, chess-playing, perhaps even our
higher-level perceptual and motor skills -- also seem to be symbolic.
In any case, when we interpret our sentences, mathematical formulas,
and chess moves (and perhaps some of our perceptual judgments and motor
strategies) as having a systematic
 meaning
or
 content,
we know at first hand that that's literally true, and not just a figure
of speech. Connectionism hence seems to be at a disadvantage in
attempting to model these cognitive capacities.

Yet it is not clear whether connectionism should for this reason aspire to
be symbolic, for the symbolic approach turns out to suffer from a
severe handicap, one that may be responsible for the limited extent of
its success to date (especially in modeling human-scale capacities) as
well as the uninteresting and ad hoc nature of the symbolic "knowledge"
it attributes to the "mind" of the symbol system. The handicap has been
noticed in various forms since the advent of computing; I have
dubbed a recent manifestation of it the "symbol grounding problem"
(Harnad 1987b).


"2. The Symbol Grounding Problem"

"2.1 The Chinese Room."
Before defining the symbol grounding problem I will give two examples
of it. The first comes from Searle's (1980) celebrated "Chinese Room
Argument," in which the symbol grounding problem is referred to as the
problem of intrinsic meaning (or "intentionality"): Searle challenges
the core assumption of symbolic AI that a symbol system able to
generate behavior indistinguishable from that of a person must have a
mind. More specifically, according to the symbolic theory of mind, if a
computer could pass the Turing Test (Turing 1964) in Chinese -- i.e.,
if it could respond to all Chinese symbol strings it receives as input
with Chinese symbol strings that are indistinguishable from the replies
a real Chinese speaker would make (even if we keep testing for a
lifetime) -- then the computer would understand the meaning of Chinese
symbols in the same sense that I understand the meaning of English
symbols.

Searle's simple demonstration that this cannot be so consists of
imagining himself doing everything the computer does -- receiving the
Chinese input symbols, manipulating them purely on the basis of their shape
(in accordance with (1) to (8) above), and finally returning the Chinese
output symbols. It is evident that Searle (who knows no Chinese) would
not be understanding Chinese under those conditions -- hence neither
could the computer. The symbols and the symbol manipulation, being all
based on shape rather than meaning, are systematically
 interpretable
as having meaning -- that, after all, is what it is to be a symbol
system, according to our definition. But the interpretation will not be
 intrinsic
to the symbol system itself: It will be parasitic on the fact that the
symbols have meaning for
 us,
in exactly the same way that the meanings of the symbols in a book are
not intrinsic, but derive from the meanings in our heads. Hence, if the
meanings of symbols in a symbol system are extrinsic, rather than
intrinsic like the meanings in our heads, then they are not a viable
model for the meanings in our heads: Cognition cannot be just symbol
manipulation.

"2.2 The Chinese/Chinese Dictionary-Go-Round."
My own example of the symbol grounding problem has two versions,
one difficult, and one, I think, impossible. The difficult version is: Suppose
you had to learn Chinese as a second language and the only source of
information you had was a Chinese/Chinese dictionary. The trip through
the dictionary would amount to a merry-go-round, passing endlessly from
one meaningless symbol or symbol-string (the definientes) to another (the
definienda), never coming to a halt on what anything meant.\**
[footnote start]



Symbolic AI abounds with symptoms of the symbol grounding problem. One
well-known (though misdiagnosed) manifestation of it is the so-called
"frame" problem
(McCarthy & Hayes 1969; Minsky 1974; NcDermott 1976; Pylyshyn 1987): It
is a frustrating but familiar experience in writing "knowledge-based"
programs that a system apparently behaving perfectly intelligently for
a while can be foiled by an unexpected case that demonstrates its utter
stupidity: A "scene-understanding" program will blithely describe the
goings-on in a visual scene and answer questions demonstrating its
comprehension (who did what, where, why?) and then suddenly reveal that
it doesn't "know" that hanging up the phone and leaving the room does
not make the phone disappear, or something like that. (It is important
to note that these are not the kinds of lapses and gaps in knowledge
that people are prone to; rather, they are such howlers as to cast
serious doubt on whether the system has anything like "knowledge" at
all.)
The "frame" problem has been optimistically defined as the problem of
formally specifying ("framing") what varies and what stays constant in
a particular "knowledge domain," but in reality it's the problem of
second-guessing all the contingencies the programmer has not
anticipated in symbolizing the knowledge he is attempting to
symbolize. These contingencies are probably unbounded, for practical
purposes, because purely symbolic "knowledge" is ungrounded. Merely
adding on more symbolic contingencies is like taking a few more turns
in the Chinese/Chinese Dictionary-Go-Round. There is in reality no
ground in sight: merely enough "intelligent" symbol-manipulation to lull
the programmer into losing sight of the fact that its meaningfulness is
just parasitic on the meanings he is projecting onto it from the
grounded meanings in his own head. (I've called this effect the
"hermeneutic hall of mirrors" [Harnad 1990]; it's the reverse side of
the symbol grounding problem). Yet parasitism it is, as the next "frame
problem" lurking around the corner is ready to confirm. (A similar form
of over-interpretation has occurred in the ape "language" experiments
[Terrace 1979]. Perhaps both apes and computers should be trained using
Chinese code, to immunize their experimenters and programmers against
spurious over-interpretations. But since the actual behavioral tasks in
both domains are still so trivial, there's probably no way to prevent
their being decrypted. In fact, there seems to be an irresistible
tendency to overinterpret toy task performance itself, preemptively
extrapolating and "scaling it up" conceptually to lifesize without any
justification in practice.)
[footnote end]



-- Figure 1 (Chinese Dictionary Entry) about here. --


The only reason cryptologists of ancient languages and secret codes
seem to be able to successfully accomplish something very like this is
that their efforts are
 grounded
in a first language and in real world experience and knowledge.\**
[footnote start]



Cryptologists also use statistical information about word frequencies,
inferences about what an ancient culture or an enemy government are
likely to be writing about, decryption algorithms, etc.
[footnote end]
The second variant of the Dictionary-Go-Round, however, goes far beyond
the conceivable resources of cryptology: Suppose you had to learn
Chinese as a
 first
language and the only source of information you had was a
Chinese/Chinese dictionary!\**
[footnote start]



There is of course no need to restrict the symbolic resources to a dictionary;
the task would be just as impossible if one had access to the entire body of
Chinese-language literature, including all of its computer programs
and anything else that can be codified in symbols.
[footnote end]
This is more like the actual task faced by
a purely symbolic model of the mind: How can you ever get off the
symbol/symbol merry-go-round? How is symbol meaning to be grounded in
something other than just more meaningless symbols?\**
[footnote start]



Even mathematicians, whether Platonist or formalist, point out that
symbol manipulation (computation) itself cannot capture the notion of the
intended interpretation of the symbols (Penrose 1989). The fact that
formal symbol systems and their interpretations are not the same thing
is hence evident independently of the Church-Turing thesis (Kleene
1969) or the Goedel results (Davis 1958, 1965), which have been zealously
misapplied to the problem of mind-modeling (e.g., by Lucas 1964) -- to
which they are largely irrelevant, in my view.
[footnote end]
This is the symbol
grounding problem.\**
[footnote start]



Note that, strictly speaking, symbol grounding is a
problem only for cognitive modeling, not for AI in general. If
symbol systems alone
succeed in generating all the intelligent machine
performance pure AI is interested in -- e.g., an automated dictionary --
then there is no reason whatsoever to demand that their symbols have
intrinsic meaning. On the other hand, the fact that our own symbols do
have intrinsic meaning whereas the computer's do not, and the fact
that we can do things that the computer so far cannot, may be
indications that even in AI there are performance gains to be made
(especially in robotics and machine vision) from endeavouring to ground
symbol systems.
[footnote end]

"2.3 Connecting to the World."
The standard reply of the symbolist (e.g., Fodor 1980, 1985) is that the
meaning of the symbols comes from connecting the symbol system to the
world "in the right way." But it seems apparent that the problem of
connecting up with the world in the right way is virtually coextensive
with the problem of cognition itself. If each definiens in a
Chinese/Chinese dictionary were somehow connected to the world in the right
way, we'd hardly need the definienda! Many symbolists believe that
cognition, being symbol-manipulation, is an autonomous functional
module that need only be hooked up to peripheral devices in order to
"see" the world of objects to which its symbols refer (or, rather, to
which they can be systematically interpreted as referring).\**
[footnote start]



The homuncular viewpoint inherent in this belief is quite apparent,
as is the effect of the "hermeneutic hall of mirrors" (Harnad 1990).
[footnote end]
Unfortunately, this radically underestimates the difficulty of picking
out the objects, events and states of affairs in the world that symbols
refer to, i.e., it trivializes the symbol grounding problem.

It is one possible candidate for a solution to this problem, confronted
directly, that will now be sketched: What will be proposed is
a hybrid nonsymbolic/symbolic
system, a "dedicated" one, in which the elementary symbols are grounded
in two kinds of nonsymbolic representations that pick out, from their
proximal sensory projections, the distal object categories to which the
elementary symbols refer. Most of the components of which the model is
made up (analog projections and transformations, discretization,
invariance detection, connectionism, symbol manipulation) have also
been proposed in various configurations by others, but they will be put
together in a specific bottom-up way here that has not, to my
knowledge, been previously suggested, and it is on this specific
configuration that the potential success of the grounding scheme
critically depends. 

Table 1 summarizes the relative strengths and weaknesses of
connectionism and symbolism, the two current rival candidates for
explaining
 all
of cognition single-handedly. Their respective strengths will be put to
cooperative rather than competing use in our hybrid model, thereby also
remedying some of their respective weaknesses. Let us now look more
closely at the behavioral capacities such a cognitive model must
generate.



-- Table 1 about here --




3. Human Behavioral Capacity


Since the advent of cognitivism, psychologists have continued to gather
behavioral data, although to a large extent the relevant
evidence is already in: We already know what human beings are able to
do. They can (1)
 discriminate,
(2)
 manipulate,\**
[footnote start]



Although they are no doubt as important as perceptual skills, motor
skills will not be explicitly considered here. It is assumed that the
relevant features of the sensory story (e.g., iconicity) will
generalize to the motor story (e.g., in motor analogs; Liberman 1982).
In addition, large parts of the motor story may not be cognitive,
drawing instead upon innate motor patterns and sensorimotor feedback.
Gibson's (1979) concept of "affordances" -- the invariant stimulus
features that are detected by the motor possibilities they "afford" --
is relevant here too, though Gibson underestimates the processing problems
involved in finding such invariants (Ullman 1980). In any case, motor
and sensory-motor grounding will no doubt be as important as the
sensory grounding that is being focused on here.
[footnote end]
(3)
 identify
and (4)
 describe
the objects, events and
states of affairs in the world they live in, and they can also (5)
 "produce descriptions"
and (6)
 "respond to descriptions"
of those objects,
events and states of affairs. Cognitive
theory's burden is now to explain
 how
human beings (or any other devices) do all this.\**
[footnote start]



If a candidate model were to exhibit all these behavioral capacities,
both
 linguistic
(5-6)
and
 robotic
(i.e., sensorimotor),
(1-3)
it would pass the
"Total Turing Test" (Harnad 1989).
The standard Turing Test (Turing 1964) calls for linguistic performance
capacity only: symbols in and symbols out. This makes it equivocal
about the status, scope and limits of pure symbol manipulation, and
hence subject to the symbol grounding problem. A model that could pass
the Total Turing Test, however, would be grounded in the world.
[footnote end]

"3.1 Discrimination and Identification."
Let us first look more closely at discrimination and identification.
To be able to
 discriminate
is to able to judge whether two inputs are
the same or different, and, if different, 
 how
different they are. Discrimination is a relative judgment, based on our
capacity to tell things apart and discern their degree of similarity. To
be able to
 identify
is to be able to assign a unique (usually arbitrary) response -- a
"name" -- to a class of inputs, treating them all as equivalent or
invariant in some respect. Identification is an absolute judgment,
based on our capacity to tell whether or not a given input is a member of a
particular
 category.

Consider the symbol "horse." We are able, in viewing different horses
(or the same horse in different positions, or at different times) to
tell them apart and to judge which of them are more alike, and
even how alike they are. This is discrimination.
In addition, in viewing a horse, we can reliably call it a horse,
rather than, say, a mule or a donkey (or a giraffe, or a stone). This
is identification. What sort of internal representation would be needed
in order to generate these two kinds of performance?

"3.2 Iconic and categorical representations."
According to the model being proposed here, our ability
to discriminate inputs depends on our forming
 "iconic representations"
of them (Harnad 1987b). These are internal analog transforms of the
projections of distal objects on our sensory surfaces (Shepard &
Cooper 1982). In the case of
horses (and vision), they would be analogs of the many shapes that horses
cast on our retinas.\**
[footnote start]



There are many problems having to do with figure/ground
discrimination, smoothing, size constancy, shape constancy,
stereopsis, etc., that
make the problem of discrimination much more complicated than what is
described here, but these do not change the basic fact that iconic
representations are a natural candidate substrate for our
capacity to discriminate.
[footnote end]
Same/different judgments would be based on the sameness or difference
of these iconic representations, and similarity judgments would be
based on their degree of congruity. No homunculus is involved here;
simply a process of superimposing icons and registering their degree
of disparity. Nor are there memory problems, since the inputs are
either simultaneously present or available in rapid enough succession
to draw upon their persisting sensory icons.

So we need horse icons to discriminate horses. But what about
identifying them? Discrimination is independent of identification. I
could be discriminating things without knowing what they were. Will the
icon allow me to identify horses? Although there are theorists who
believe it would (Paivio 1986), I have tried to show why it could not
(Harnad 1982, 1987b). In a world where there were bold, easily
detected natural discontinuities between all the categories we would
ever have to (or choose to) sort and identify -- a world in which the
members of one category couldn't be confused with the members of any
another category -- icons might be sufficient for identification. But
in our underdetermined world, with its infinity of confusable potential
categories, icons are useless for identification because there are too
many of them and because they blend continuously\**
[footnote start]



Elsewhere (Harnad 1987a,b) I have tried to show how the phenomenon of
"categorical perception" could generate internal discontinuities where
there is external continuity. There is evidence that our perceptual
system is able to segment a continuum, such as the color spectrum, into
relatively discrete, bounded regions or categories. Physical
differences of equal magnitude are more discriminable across the
boundaries between these categories than within them. This boundary
effect, both innate and learned, may play an important role in the
representation of the elementary perceptual categories out of which the
higher-order ones are built.
[footnote end]
into one another, making it an independent problem to
 identify
which of them are icons of members of the category and which are not!
Icons of sensory projections are too unselective. For identification,
icons must be selectively reduced to those
 "invariant features"
of the sensory projection that
will reliably distinguish a member of a category from any nonmembers
with which it could be confused. Let us call the output of this
category-specific feature detector the
 "categorical representation" .
In some cases these representations may be innate, but
since evolution could hardly anticipate all of
the categories we may ever need or choose to identify, most of these
features must be learned from experience. In particular,
our categorical representation of a horse is probably a learned one.
(I will defer till section 4 the problem of how the invariant features
underlying identification might be learned.)

Note that both iconic and categorical representations are nonsymbolic.
The former are analog copies of the sensory projection, preserving
its "shape" faithfully; the latter are icons that have been
selectively filtered to preserve only some of the features of the shape
of the sensory projection: those that reliably distinguish members from
nonmembers of a category. But both representations are still sensory
and nonsymbolic. There is no problem about their connection to the
objects they pick out: It is a purely causal connection, based on the
relation between distal objects, proximal sensory projections and the
acquired internal changes that result from a history of behavioral
interactions with them. Nor is there any problem of semantic
interpretation, or whether the semantic interpretation is justified.
Iconic representations no more "mean" the objects of which they are the
projections than the image in a camera does. Both icons and
camera-images can of course be
 interpreted
as meaning or standing for something, but the interpretation would
clearly be derivative rather than intrinsic.\**
[footnote start]



On the other hand, the resemblance on which discrimination performance
is based -- the degree of isomorphism between the icon and the sensory
projection, and between the sensory projection and the distal object --
seems to be intrinsic, rather than just a matter of interpretation. The
resemblance can be objectively characterized as the degree of
invertibility of the physical transformation from object to icon (Harnad 1987b).
[footnote end]

"3.3 Symbolic Representations."
Nor can categorical representations yet be interpreted as "meaning"
anything. It is true that they pick out the class of objects they
"name," but the names do not have all the systematic properties of symbols
and symbol systems described earlier. They are just an inert taxonomy.
For systematicity it must be possible to combine and recombine them 
rulefully into
propositions that can be semantically interpreted. "Horse" is so far
just an arbitrary response that is reliably made in the presence
of a certain category of objects. There is
no justification for interpreting it holophrastically as meaning "This
is a [member of the category] horse" when produced in the presence of a
horse, because the other expected systematic properties of "this" and
"a" and the all-important "is" of predication are not exhibited by mere
passive taxonomizing. What would be required to generate these other
systematic properties? Merely that the 
grounded names in the category taxonomy be
strung together into 
 propositions
about further category
membership relations. For example:

(1) Suppose the name "horse" is grounded by iconic and categorical
representations, learned from experience, that reliably discriminate
and identify horses on the basis of their sensory projections.

(2) Suppose "stripes" is similarly grounded.

Now consider that the following category can be constituted out of
these elementary categories by a symbolic description of category
membership alone:

(3) "Zebra" = "horse" & "stripes"\**
[footnote start]



Figure 1 is actually the Chinese dictionary entry for "zebra," which
is "striped horse." Note that the character for "zebra" actually happens
to be the character for "horse" plus the character for "striped."
Although Chinese characters are iconic in structure, they function
just like arbitrary alphabetic lexigrams at the level of syntax and
semantics.
[footnote end]

What is the representation of a zebra? It is just the symbol string
"horse & stripes." But because "horse" and "stripes" are grounded in their
respective iconic and categorical representations, "zebra"
inherits the grounding, through its grounded
 symbolic
representation.
In principle, someone who had never seen a zebra (but had seen
and learned to identify horses and stripes) could identify a zebra on first
acquaintance armed with this symbolic representation alone (plus the
nonsymbolic -- iconic and categorical -- representations of horses and
stripes that ground it).

Once one has the grounded set of elementary symbols provided
by a taxonomy of names (and the iconic and categorical
representations that give content to the names and allow them to pick
out the objects they identify), the rest of the symbol strings
of a natural language can be generated by symbol composition alone,\**
[footnote start]



Some standard logical connectives and quantifiers are needed
too, such as not, and, all, etc.
[footnote end]
and they will all inherit the intrinsic grounding of the elementary set.\**
[footnote start]



Note that it is not being claimed that
"horse," "stripes," etc. are actually elementary symbols, with direct
sensory grounding; the claim is only that
 some
set of symbols must be directly grounded. Most sensory category
representations are no doubt hybrid sensory/symbolic; and their
features can change by bootstrapping: "Horse" can always be revised, both
sensorily and symbolically, even if it was previously elementary.
Kripke (1980) gives a good example of how "gold" might be baptized on
the shiny yellow metal in question, used for trade, decoration and
discourse, and then we might discover "fool's gold," which would make
all the sensory features we had used until then inadequate, forcing us
to find new ones. He points out that it is even possible in principle
for "gold" to have been inadvertently baptized on "fool's gold"! Of
interest here are not the ontological aspects of this possibility, but
the epistemic ones: We could bootstrap successfully to real gold even if every
prior case had been fool's gold. "Gold" would still be the right
word for what we had been trying to pick out all along, and its
original provisional features would still have provided a close enough
approximation to ground it, even if later information were to pull the
ground out from under it, so to speak.
[footnote end]
Hence, the ability to discriminate and categorize (and its
underlying nonsymbolic representations) has led naturally to the ability
to describe and to produce and respond to descriptions through
symbolic representations.



4. A Complementary Role for Connectionism


The symbol grounding scheme just described has one prominent gap: No
mechanism has been suggested to explain how the all-important
categorical representations could be formed: How does the hybrid system
find the invariant features of the sensory projection that make it
possible to categorize and identify objects correctly?\**
[footnote start]



Although it is beyond the scope of this paper to discuss it at length,
it must be mentioned that this question has often been begged in the
past, mainly on the grounds of "vanishing intersections." It has been
claimed that one cannot find invariant features in the sensory
projection because they simply do not exist: The intersection of all
the projections of the members of a category such as "horse" is empty.
The British empiricists have been criticized for thinking otherwise;
for example, Wittgenstein's (1953) discussion of "games" and "family
resemblances" has been taken to have discredited their view. And
current research on human categorization (Rosch & Lloyd 1978) has been
interpreted as confirming that intersections vanish and that hence
categories are not represented in terms of invariant features. The
problem of vanishing intersections (together with Chomsky's [1980]
"poverty of the stimulus argument") has even been cited by thinkers
such as Fodor (1985, 1987) as a justification for extreme nativism. The
present paper is frankly empiricist. In my view, the reason
intersections have not been found is that no one has yet looked for
them properly. Introspection certainly isn't the way to look. And
general pattern learning algorithms such as connectionism are
relatively new; their inductive power remains to be tested. In
addition, a careful distinction has not been made between pure sensory
categories (which, I claim, must have invariants, otherwise we could
not successfully identify them as we do) and higher-order categories
that are
 grounded
in sensory categories; these abstract representations may be symbolic
rather than sensory, and hence not based directly on sensory
invariants. For further discussion of this problem, see Harnad 1987b).
[footnote end]
Connectionism, with its general pattern learning capability, seems to
be one natural candidate (though there may well be others): Icons, paired with
feedback indicating their names, could be processed by a connectionist
network that learns to identify icons correctly from the sample of
confusable alternatives it has encountered by dynamically adjusting the
weights of the features and feature combinations that are reliably
associated with the names in a way that (provisionally) resolves the
confusion, thereby reducing the icons to the
 invariant
(confusion-resolving) features of the category to which they are
assigned. In effect, the "connection" between the names and the objects
that give rise to their sensory projections and their icons would be
provided by connectionist networks.

This circumscribed complementary role for connectionism in a hybrid
system seems to remedy the weaknesses of the two current competitors
in their attempts to model the mind independently.
In a pure symbolic model the crucial connection between
the symbols and their referents is missing; an autonomous symbol
system, though amenable to a systematic semantic interpretation, is
ungrounded.
In a pure connectionist model, names are connected to
objects through invariant patterns in their sensory projections,
learned through exposure and feedback, but the crucial compositional
property is missing; a network of names, though grounded, is not
yet amenable to a full systematic semantic interpretation.
In the hybrid system proposed here, there is no longer any autonomous
symbolic level at all; instead, there is an intrinsically
 dedicated
symbol system, its elementary symbols (names) connected to nonsymbolic
representations that can pick out the objects to which they refer, via
connectionist networks that extract the invariant features of their
analog sensory projections.



5. Conclusions


The expectation has often been voiced that "top-down" (symbolic)
approaches to modeling cognition will somehow meet "bottom-up"
(sensory) approaches somewhere in between. If the grounding
considerations in this paper are valid, then this expectation is
hopelessly modular and there is really only one viable route from sense
to symbols: from the ground up. A free-floating symbolic level like the
software level of a computer will never be reached by this route (or
vice versa) -- nor is it clear why we should even try to reach such a level,
since it looks as if getting there would just amount to uprooting our
symbols from their intrinsic meanings (thereby merely reducing
ourselves to the functional equivalent of a programmable computer).

In an intrinsically dedicated symbol system there are more constraints
on the symbol tokens than merely syntactic ones. Symbols are
manipulated not only on the basis of the arbitrary shape of their
tokens, but also on the basis of the decidedly nonarbitrary
"shape" of the iconic and categorical representations connected to
the grounded elementary symbols out of which the higher-order
symbols are composed. Of these two kinds of constraints, the
iconic/categorical ones are primary. I am not aware of any
formal analysis of such dedicated symbol systems,\**
[footnote start]



Although mathematicians investigate the formal properties of
uninterpreted symbol systems, all of their motivations and intuitions
clearly come from the intended interpretations of those systems (see
Penrose 1989). Perhaps these too are grounded in the iconic and
categorical representations in their heads.
[footnote end]
but this may be
because they are unique to cognitive and robotic modeling and their
properties will depend on the specific kinds of robotic (i.e., behavioral)
capacities they are designed to exhibit.

It is appropriate that the properties of dedicated symbol systems
should turn out to depend on behavioral considerations. The present
grounding scheme is still in the spirit of behaviorism in that the
only tests proposed for whether a semantic interpretation will bear the
semantic weight placed on it consist of one formal test (does it meet
the eight criteria for being a symbol system?) and one behavioral test
(can it discriminate, identify and describe all the objects and states
of affairs to which its symbols refer?). If both tests are passed, then
the semantic interpretation of its symbols is "fixed" by the behavioral
capacity of the dedicated symbol system, as exercised on the objects
and states of affairs in the world to which its symbols refer; the
symbol meanings are accordingly not just parasitic on the meanings in the
head of the interpreter, but intrinsic to the dedicated symbol system
itself. This is still no guarantee that our model has captured subjective
meaning, of course. But if the system's behavioral capacities are
lifesize, it's as close as we can ever hope to get.






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This figure should consist of the Chinese
characters for "zebra," "horse" and "stripes," formatted
as a dictionary entry, thus:

"ZEBRA": "HORSE" with "STRIPES"

Table 1. Connectionism Vs. Symbol Systems


Strengths of Connectionism:



(1) Nonsymbolic Function:

As long as it does not aspire to be a symbol system, a connectionist
network has the advantage of not being subject to the symbol grounding
problem.


(2) Generality:

Connectionism applies the same small family of algorithms to many problems,
whereas symbolism, being a methodology rather than an algorithm, relies
on endless problem-specific symbolic rules.


(3) "Neurosimilitude":

Connectionist architecture seems more brain-like than a
Turing machine or a digital computer.


(4) Pattern Learning:

Connectionist networks are especially suited to the learning of
patterns from data.


Weaknesses of Connectionism:



(1) Nonsymbolic Function:

Connectionist networks, because they are not symbol systems, do not
have the systematic semantic properties that many cognitive phenomena
appear to have.


(2) Generality:

Not every problem amounts to pattern learning. Some cognitive tasks
may call for problem-specific rules, symbol manipulation, and
standard computation.


(3) "Neurosimilitude" :

Connectionism's brain-likeness may be superficial and may (like toy
models) camoflauge deeper performance limitations.


Strengths of Symbol Systems:




(1) Symbolic Function:

Symbols have the computing power of Turing Machines and
the systematic properties of a formal syntax that is semantically
interpretable.


(2) Generality:

All computable functions (including all cognitive functions) are
equivalent to a computational state in a Turing Machine.


(3) Practical Successes:

Symbol systems' ability to generate intelligent behavior is
demonstrated by the successes of Artificial Intelligence.


Weaknesses of Symbol Systems:



(1) Symbolic Function:

Symbol systems are subject to the symbol grounding problem.


(2) Generality:

Turing power is too general. The solutions to AI's many toy problems do
not give rise to common principles of cognition but to a vast variety
of ad hoc symbolic strategies.